I think that this could work, but I think that the draw odd on the public portion would be dismal. Most people would put in for the public tag first and the ones with access to private would likely be able to draw the private tag second choice. This is what I would do.
I think that a better solution is rework the unit boundaries so that land owner ship in the unit is more consistent. Kind of like how politicians draw voting districts. Some units would be heavily public and others would be heavily private and only a few would be a mix of both. There is always going to be some private land that fits into the public units and some isolated public land in the private units. For example, Why is FWP including unit 702 with 704?The is very little accessible public in 702 and the Custer is in 704. Combining the two all but guarantees that some people that have access to land in 702 will not have a tag and that the Custer is going to be over hunted. For that matter why is 704 so big? The northern part of 704 has relatively little accessible public and the southern part which contains the Custer has quite a bit of accessible public.
@Gerald Martin is getting at the root of the problem when he talks about FWP relying on hunters to distribute pressure themselves. Maybe that worked in the 70's but it doesn't work today. As long as FWP continues to rely on the law of diminishing returns to regulate hunting pressure there is going to be issues.
I understand that by drawing up units like this, the odds on the mostly public units would not be good, but unlike were you have just a public and a private unit the public hunter would not be out of luck if they did not draw. My bet is that the public hunter could pick up a mostly private unit second or third choice. Granted they would have to hunt a small isolated bit of public or get in line on some BM ranch but you would still get to hunt most years, just not your first choice unit.